{"paper":{"title":"Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and Two-Dimensional $O(N)$-Symmetric Nonlinear $\\sigma$-Models","license":"","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Alan D. Sokal (New York University), Andrea Pelissetto, Tereza Mendes","submitted_at":"1996-04-18T17:21:30Z","abstract_excerpt":"We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $\\sigma$-models. We then apply the method to the two-dimensional $O(N)$-symmetric nonlinear $\\sigma$-models (also called $N$-vector models) with $N=3,4,8$ and study its dynamic critical behavior. Using lattices up to $256 \\times 256$, we find dynamic critical exponents $z_{int,{\\cal M}^2} \\approx 0.70 \\pm 0.08$, $0.60 \\pm 0.07$, $0.52 \\pm 0.10$ for $N=3,4,8$, respectively (subjective 68\\% confidenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9604015","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}